Method of digitally processing optical waves in integrated planar optical devices that operate on the principle of digital planar holography

ABSTRACT

A method of digitally processing light waves passing through a planar structure having given functions f in (x, y, ω) and f out (x, y, ω) and consisting of a light-propagating and distributing layer. This layer contains a plurality of interconnecting pattern elements of a holographic pattern and a plurality of planar optical elements arranged in a predetermined pattern on the aforementioned light-propagating and distributing layer. The method consists of calculating positions and shapes of the interconnecting pattern elements of the holographic pattern based on the aforementioned given functions by solving an inverse problem. The interconnecting pattern elements have refractive indices different from the refractive indices of the light-propagating and distributing layer and are manufactured on the basis of the results of the calculations. The aforementioned continuous function is digitized, and the obtained digitized planar holographic pattern is used for converting the function f in (x, y, ω) into the function f out (x, y, ω).

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is division of U.S. patent application Ser. No.12/011,453 filed Jan. 28, 2008 and entitled “Method of DigitallyProcessing Optical Waves and an Integrated Planar Optical Device Basedon Digital Planar Holography”

FIELD OF THE INVENTION

This invention relates to the processing of light or other waves insideplanar integrated circuits consisting of a plurality of repeatedstandard elements such as lasers, amplifiers, detectors, and fastsaturated absorbers, interconnected through digital planar holograms.More specifically, the invention relates to a method of digitallyprocessing optical waves in integrated planar optical devices thatoperate on the principle of digital planar holography.

BACKGROUND OF THE INVENTION

Processing and transmission of information with light requires creationof integrated optical circuits. While the idea is not novel, integratedcircuits with the use of light do not repeat the success of electronicintegrated circuits, while most important active and non-linear opticelements like lasers, amplifiers, detectors, and fast saturatingabsorbers, are routinely made in planar waveguides withmicrolithography, then diced and connected with optical fibers. It ismuch like the use of transistors before the invention of electronicintegrated circuits. One of the main reasons is the problem ofinterconnection. Electric current easily follows through bends of aconductor, thereby facilitating interconnections among several layers.The light tends to propagate in a straight line; therefore,interconnections among several layers are difficult. Sometimes activeelements are interconnected by ridge waveguides in a single waveguide,but this method is limited due to the crossing of ridge waveguides in asingle layer. Thus, there is a great need for interconnecting manyoptical elements in a single waveguide.

Attempts have been made heretofore to provide planar optical devices byinterconnecting many optical devices on a single substrate. For example,U.S. Patent Application Publication No. 20070034730 published in 2007(inventor T. Mossberg, et al.) discloses a method that comprises thesteps of forming a planar optical waveguide that confines in onetransverse spatial dimension an optical signal propagating in two otherspatial dimensions, and forming a set of diffractive elements in theplanar optical waveguide. The latter is arranged so as to supportmultiple optical transverse modes in the confined transverse dimension.Each diffractive element set is arranged so as to route, between acorresponding input optical port and a corresponding output opticalport, a corresponding diffracted portion of the optical signalpropagating in the planar waveguide that is diffracted by thediffractive element set. The diffractive elements are arranged so thatthe optical signal is successively incident on the diffractive elements;and the diffractive elements and the planar optical waveguide arearranged so that the corresponding diffracted portion of the opticalsignal reaches the corresponding output optical port as a superpositionof multiple optical transverse modes supported by the planar opticalwaveguide.

U.S. Patent Application Publication No. 20060233493 published in 2006(inventor T. Mossberg, et al.) discloses a method comprising the stepsof receiving an input optical signal successively incident on a set ofdiffractive elements in an optical medium. The optical medium enablessubstantially unconfined propagation of optical signal in threedimensions. At least a portion of the input optical signal passesthrough the set of diffractive elements and produces an output opticalsignal. The diffractive elements of the set are collectively arrangedwithin the slab waveguide so as to exhibit a positional variation inamplitude, optical separation, or spatial phase over some portion of theset. Furthermore, the diffractive elements of the set collectively applya transfer function to the input optical signal for producing the outputoptical signal, the transfer function being determined at least in partby said positional variation in amplitude, optical separation, orspatial phase exhibited by the diffractive elements of the set.

U.S. Patent Application Publication No. 20070053635 published in 2007(inventor D. Lazikov, et al) discloses a method that comprises computingan interference pattern between a simulated design input optical signaland a simulated design output optical signal, and computationallyderiving an arrangement of at least one diffractive element set from thecomputed interference pattern. The interference pattern is computed in atransmission grating region, with the input and output optical signalseach propagating through the transmission grating region assubstantially unconfined optical beams. The arrangement of diffractiveelement set is computationally derived so that when the diffractiveelement set thus arranged is formed in or on a transmission grating,each diffractive element set would route, between corresponding inputand output optical ports, a corresponding diffracted portion of an inputoptical signal incident on and transmitted by the transmission grating.The method can further comprise forming the set of diffractive elementsin or on the transmission grating according to the derived arrangement.

U.S. Patent Application Publication No. 20060126992 published in 2006(inventor T. Hashimoto, et al.) discloses a wave transmission mediumthat includes an input port and an output port. The first and the secondfield distributions are obtained by numerical calculations. The firstfield distribution distributes the forward propagation light launchedinto the input port. The second field distribution distributes thereverse propagation light resulting from reversely transmitting from theoutput port side an output field that is sent from the output port whenan optical signal is launched into the input port. A spatial refractiveindex distribution is calculated on the basis of both fielddistributions such that the phase difference between the propagationlight and reverse propagation light is eliminated at individual points(x, z) in the medium. The elements of this system are also mounted on aplanar substrate.

U.S. Patent Application Publication No. 20040036933 published in 2004(inventor V. Yankov, et al.) discloses a method and device that provideefficient wavelength division multiplexing/demultiplexing (WDM)including reduced signal distortion, higher wavelength selectivity,increased light efficiency, reduced cross-talk, and easier integrationwith other planar devices, and lower cost manufacturing. The method anddevice include a planar holographic multiplexer/demultiplexer having aplanar waveguide, the planar waveguide including a holographic elementthat separates and combines pre-determined (pre-selected) lightwavelengths. The holographic element includes a plurality of hologramsthat reflect pre-determined light wavelengths from an incoming opticalbeam to a plurality of different focal points, each pre-determinedwavelength representing the center wavelength of a distinct channel.Advantageously, a plurality of superposed holograms may be formed by aplurality of structures, each hologram reflecting a distinct centerwavelength to represent a distinct channel to provide discretedispersion. When used as a demultiplexer, the holographic elementspatially separates light of different wavelengths and when reversingthe direction of light propagation, the holographic element may be usedas a multiplexer to focus several optical beams having differentwavelengths into a single beam containing all of the differentwavelengths.

However, in all aforementioned prior-art devices, for transformation ofan input beam into an output beam, the inventors use holographicgratings with known functional properties determined by their parametersand geometry. Therefore, positions and optical parameters of the inputand output beams strictly depend on the geometry of the grating, andthis significantly limits design of the optical structure. Anotherdisadvantage of the known methods and planar holographic devices is thatthey can provide a limited number of light-transmitting channels sinceeach holographic pattern element works only with one or two channels.

BRIEF SUMMARY OF THE INVENTION

The method of the invention for digitally processing light waves passingthrough a digital planar holographic structure consists of makingdigital and analog light processors on a single chip consisting of aplanar waveguide with several standard optical elements repeated manytimes. According to the invention, there may be active and nonlinearelements like lasers, amplifiers, and fast saturated absorbers that aremade in planar semiconductor waveguides by microlithography means andthat are interconnected by passive digital planar holograms written inthe same waveguide. Each hologram can provide many interconnections. Theplanar waveguide can be monolithic; for example, the core can be madefrom a semiconductor like InPGaAs. The difference among lasers,amplifiers, and fast-saturated absorbers may be due to differentvoltages applied to these elements, different geometry, or chemicalcomposition. Since light absorption in semiconductor holograms creates aproblem, it may be eased by applying voltage to holograms or making ahybrid waveguide. Namely, active elements can be made in a semiconductorwaveguide, while interconnecting holograms may be written in an attachedtransparent waveguide made of silica or another transparent material.

A hologram is a combination of millions of sub-wavelength (a fraction ofmicron) features recorded on a transparent media. A hologram may be acopy of an image or even of an optical device. After replicating anoptical device, the hologram may be used instead of the device. Untilthe 1990s, analog holograms were made with conventional photo materials,copying existing objects only. Digital holography has been made possiblewhen microlithography moved to sub-micron features. By means ofcalculations, it becomes possible to determine positions of holographicfringes. If the shape of a planar structure is known, as well as thepositions of the input and output light beams, the finding ofhologram-component coordinates is reduced to the solution of an inverseproblem of finding a part of the boundary conditions based on the knownfunctions f_(in)(x, y, ω) and f_(out)(x, y, ω), the structures, shapes,and positions of which have been calculated and which have never existedin reality as optical objects and which are then reproduced by methodsof microlithography in the form of actual planar objects.

An inverse problem can be defined as a task wherein the values of somemodel parameter(s) must be obtained from the observed data.

In particular, the invention relates to the digital processing oflights, wherein chains of lasers, amplifiers, and fast saturatingabsorbers exhibit two or more attractors. A light logical gate is oneexample of a device that can be made by this new technology.

The approach of this invention is to characterize a device by Fouriercomponents f_(in)(x, y, ω) and f_(out)(x, y, ω) of incoming and outgoingwaves propagating between two elements and then to use these functionsfor calculating a desirable holographic pattern. For most applications,it is a variation of the effective refractive index in the followingform:

Δn(x, y)=∫f _(in)(x, y, ω) f _(out)(x, y, ω) dω.

The proposed invention advantageously combines convenience ofmanufacturing and interconnecting optical elements within a singleplanar waveguide.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view that exemplifies a planar structure or aholographic chip of the invention with a digital planar opticalholographic pattern.

FIG. 2 is a longitudinal sectional view of the laser diode used in theholographic chip of FIG. 1.

FIG. 3 is a longitudinal sectional view of the planar semiconductoramplifier used in the holographic chip of FIG. 1.

FIG. 4 is a sectional view through the chip in the direction of thelongitudinal axis of the planar semiconductor light-beam receiver.

DETAILED DESCRIPTION OF THE INVENTION

The idea of the new planar geometry is to allow light to travel inside ahologram on thousands of wavelengths, thus greatly increasing thepossibility to process the light.

Digital planar holography advantageously combines the possibility towrite an arbitrary hologram with a long light path inside the hologram.The last technological obstacle was a good-quality blank planarwaveguide. The waveguide must be approximately one micron thick,transparent, and very uniform in order to transmit light withoutdistortion. The last condition is the most limiting, but it was mainlyresolved by the optical industry to make arrayed waveguide gratings foroptical fiber communication devices. After the problems associated withfabrication of sub-wavelength patterns were solved due to the progressin modern microlithography, only one problem needed for successfulrealization of the digital planar holography remained, i.e., determiningthe pattern to be written in order to make a desirable device.

By means of calculations, it becomes possible to determine the positionsof holographic fringes. If the shape of the planar structure is known,as well as the positions of the input and output light beams, thefinding of holographic pattern coordinates is reduced to the solution ofan inverse problem of finding a part of the boundary conditions based onthe known functions f_(in)(x, y, ω) and f_(out)(x, y, ω), an thestructures, shapes, and positions of which have been calculated andwhich have never existed in reality as optical objects and which arethen reproduced by methods of microlithography in the form of actualplanar objects.

The approach of this invention is to characterize a device by Fouriercomponents f_(in)(x, y, ω) and f_(out)(x, y, ω) of incoming and outgoingwaves and then to use these functions for calculating a desirableholographic pattern. While real devices are three-dimensional, using atwo-dimensional Hamiltonian model averaged over the third dimensionshould be satisfactory for many applications. Since waves propagatefreely in a blank waveguide, it becomes possible to write interaction inthe form of a Hamiltonian model. Since non-linear wave scattering can beneglected so that the Hamiltonian model can be presented as quadraticwith respect to wave amplitude, we can assume linearity with respect tovariations of the effective refraction index. Thus the Hamiltonian modelcan be written as follows:

H _(int)=∫f(x, y, ω) Δn(x, y)f(x, y, ω)d ω

where f(x, y, ω) is the total wave function of specified frequency.Since all three functions under the integral sign are oscillating, theinteraction is determined by resonances. It may be shown that in orderto transform f_(in)(x, y, ω) into f_(out)(x, y, ω) one has to createvariation of the effective refraction index, in arbitrary units, in thefollowing form:

Δn(x, y)=∫f _(in)(x, y, ω)f _(out)(x, y, ω)dω

Many variations of the invention will be possible to those skilled inthe art. Some variations include correcting the above formula forvariation of f_(in)(x, y, ω) and f_(out)(x, y, ω) created by thehologram. To ease manufacturing, the function Δn(x, y) should besubstituted by binary (two-level) functions, preferably a composition ofsimilar or identical elements. In other words, it is necessary toreplace the continuous function Δn=Δn (x, y) by a discrete function ofΔn (x, y).

This procedure can be formulated as follows:

${f_{i\; n}( {x,y,\omega} )} \cong {\sum\limits_{n,u}{C_{n\; u}{\exp ( {{ik}_{n}r_{u}} )}{f(\omega)}}}$${f_{out}( {x,y,\omega} )} \cong {\sum\limits_{m,v}{C_{m\; v}{\exp ( {{- {ik}_{m}}r_{v}} )}{f(\omega)}}}$

where k_(n) is the wave vector of an incoming wave, and r_(u) is thedistance from the incoming port number u to a current point; k_(m) isthe wave vector of an outgoing wave, and r_(v), is the distance from theoutgoing port number v to the current point; It should be noted thataccording to the invention, digitization of planar holography consistsof replacing the continuous functions f_(in)(x, y, ω) and f_(out)(x, y,ω) by finite numbers (“n” and “m”) of values as a result ofdecomposition into the Fourier series. This decomposition is used forreplacing f_(in)(x, y, ω) and f_(out)(x, y, ω) in the aforementionedformula Δn(x, y)=∫f_(in)(x, y, ω)f_(out)(x, 6, 107 )dω. It is clear thatinstead of a continuous function Δn=Δn (x, y), we will obtain a discretenumber of values of An associated with predetermined coordinates thatdetermine positions of the pattern elements of the holographic pattern.

In order to simplify production of the planar digital structure, in theaforementioned calculations, variation of the effective refractive indexΔn(x, y) can be approximated by a two-level binary function to form thepattern elements of the holographic pattern, e.g., as rectangulardashes.

In particular, the invention relates to the digital processing of light,wherein chains of lasers, amplifiers, and fast saturating absorbersexhibit two or more attractors. A light logical gate is one example of adevice that can be made according to this new technology.

Further aspects of the invention will become apparent when consideringthe drawings and the ensuing description of the preferred embodiments ofthe invention.

FIG. 1 is a schematic view that exemplifies a planar structure or aholographic chip with a digital planar optical holographic pattern. Inthis drawing, the planar structure as a whole is designated by referencenumeral 10. Reference numerals 12 _(a), 12 _(b), . . . 12 _(p),designate active planar optical elements such as semiconductor laserdiodes, where “p” is the number of the aforementioned lasers diodes.Although FIG. 1 shows only three laser diodes (p=3), the number “p” mayvary in a wide range. Reference numerals 14 a, 14 b, . . . 14 fdesignate planar semiconductor amplifiers, where “f” is the number ofsuch semiconductor amplifiers. As in the case of laser diodes, thenumber “f” may vary in a wide range. The holographic chip 10 of theillustrated embodiment also contains planar semiconductor receivers 16a, 16 b, . . . 16 g, where “g” is the number of semiconductor receivers.

All above-mentioned planar optical elements are arranged on a commonsemiconductor substrate made from, e.g., InPGaAs and, depending on thetype of the element, may have one or two input/output ports. Forexample, as shown in FIG. 1, the semiconductor laser diode 12 a has onlyan output port 12 a 1 for emission of an output light beam 12 a-out. Inthe present embodiment, it is assumed that all three laser diodes 12 a,12 b, and 12 p are identical and have respective output ports 12 a 2 and12 p for emission of output light beams 12 b-out and 12 p-out,respectively. Each of the planar semiconductor amplifiers 14 a, 14 b, .. . 14 f has one input port and one output port. For example, the planarsemiconductor amplifier 14 a has an input port 14 a 1 and an output port14 a 2; the planar semiconductor amplifier 14 b has an input port 14 a 1and an output port 14 b 2; and the planar semiconductor amplifier 14 fhas an input port 14 f 1 and an output port 14 f 2. In FIG. 1, referencenumerals 14 a-in, 14 b-in, and 14 f-in designate input light beams thatenter respective amplifiers 14 a, 14 b, and 14 f. Reference numerals 14a-out, 14 b-out, and 14 f-out designate output light beams that exitrespective amplifiers 14 a, 14 b, and 14 f.

On the other hand, each of the planar semiconductor receivers 16 a, 16b, . . . 16 g has only an input port. In other words, the planarsemiconductor receiver 16 a has an input port 16 a 1, the planarsemiconductor receiver 16 b has an input port 16 b 1, and the planarsemiconductor receiver 16 g has an input port 16 g 1. Reference numerals16 a-in, 16 b-in, and 16 g-in designate input light beams that enterrespective planar semiconductor receivers 16 a, 16 b, . . . 16 g.

In FIG. 1, reference numerals 18 a, 18 b, 18 k designate interconnectingpattern elements of the holographic pattern, which, according to theinvention, controls directions and properties of the light beamsdistributed over the entire planar structure of the chip 10 inaccordance with the aforementioned holographic pattern. As mentionedabove, for simplification of calculations and production, these patternelements are made in the form of rectangular dashes of the type shown inFIG. 1.

FIG. 1 is a generalized topology of a typical digital planar holographicchip of the present invention that shows arrangement of the optical andholographic elements and interaction therewith. It should be noted thatthe optical elements of three types shown in FIG. 1 do not limit thescope of the invention and that active and passive elements of othertypes also may be used, such as frequency multipliers, modulators,attenuators, frequency mixers, etc. More detailed structures of theplanar laser diode 12 a, a planar semiconductor amplifier 14 a, and aplanar semiconductor receiver 16 a are shown in FIGS. 2, 3, and 4,respectively. Since all of the lasers are identical, all of theamplifiers and receivers are identical as well; therefore, only onetypical representative of each of these devices is shown in therespective drawings.

As shown in FIG. 2, which is a sectional view through the chip 10 in thedirection of the longitudinal axis of the laser diode 12 a, the latteris formed on a semiconductor substrate 21 and has a planar opticalresonator 24 that emits from its edge (edge-emitting) an optical beam,from which the micro-optical system 26 forms a diffractively limitedoptical beam. The latter is introduced into the light-propagating anddistributing layer 22 that contains the aforementioned elements 18 a, 18b, . . . 18 k of the digital holographic pattern. Reference numeral 28designates an optical microprism, which together with the micro-opticalsystem 26, forms the aforementioned output port 12 a 1. Thelight-propagating and distributing layer 22 is supported by a lowercladding 20 of the holographic chip 10 and is coated with an uppercladding 23. The elements 18 a, 18 b, . . . 18 k of the digitalholographic pattern are made in flash with the surface of thelight-propagating and distributing layer 22. As mentioned above,according to the invention, the respective elements 18 a, 18 b, . . . 18k of the digital holographic pattern have specific refractive indicesdifferent from refractive indices of the layers 22 and 23. The geometryand orientations of the aforementioned elements 18 a, 18 b, . . . 18 kcontrol the characteristics and directions of the light beams that passthrough these elements.

FIG. 3 is a sectional view through the chip 10 in the direction of thelongitudinal axis of the semiconductor amplifier 14 a. Since the planarsemiconductor amplifier 14 a is located in the same chip 10, thesubstrate, cladding layers, etc., will be the same as in the case of thesemiconductor laser diode, and their description will be omitted. Thedifference between the semiconductor amplifier 14 a and thesemiconductor laser diode 12 a is that the amplifier has one input port14 a 1 and one output port 14 a 2. It is understood that the groups 34and 36 of the elements of the digital holographic pattern will bedifferent from those related to the semiconductor laser diode 12 a. Inother words, elements of the group 34 participate in control of theinput light beam 14 a-in (FIG. 1), while elements of the group 36participate in control of the output light beam 14 a-in.

FIG. 4 is a sectional view through the chip 10 in the direction of thelongitudinal axis of the planar semiconductor light-beam receiver 16 a.Since the planar semiconductor light-beam receiver 16 a is located inthe same chip 10, the substrate, cladding layers, etc., will be the sameas in the case of the semiconductor laser diode, and their descriptionswill be omitted. The difference between the semiconductor light-beamreceiver 16 a and other planar semiconductor optical elements is thatthe receiver 16 a has only one light-receiving port 16 a 1. It isunderstood that the group 38 of the elements of the digital holographicpattern will be different from those related to the semiconductor laserdiode 12 a and the semiconductor amplifier 14 a. In other words,elements of the group 38 participate in control of the input light beam16 a-in (FIG. 1).

Physically, the aforementioned elements of the digital holographicpattern 18 a, 18 b, . . . 18 k (FIG. 1), which include all groups 34,36, and 38 shown in FIGS. 2 and 3, comprise grooves formed in thelight-propagating and distributing layer 22, which are filled with anoptical material different from the material having a refractive indexdifferent from that of other structural layers of the chip 10. Theaforementioned elements may also be made in the form of metallic ordielectric stripes, recesses, projections, grooves, etc., or any otherelements that can be produced by optical, e-beam, or other type ofmicrolithography, or by nanoprinting on a planar substrate made from,e.g., a semiconductor material. Longitudinal dimensions of the patternelements 18 a, 18 b, . . . 18 k may be in the range from fractions ofmicrons to dozens of microns. Transverse dimensions may range from afraction of a micron to several microns. It is understood that theseranges are given only as examples.

In operation, pattern elements 18 a, 18 b, . . . 18 k control directionof propagating light, i.e., function in accordance with a given law asΔn=Δn(x, y). As a result, it becomes possible to replace the continuousfunction of conversion of f_(in)(x, y, ω) into f_(out)(x, y, ω) by afinite and discrete number of elements (holographic patterns) on aplanar substrate.

Thus, it has been shown that the present invention provides a new methodof making digital and analog light processors on a single chipconsisting of a planar waveguide with several standard elements repeatedmany times. The invention also provides an integrated planar opticaldevice based on digital planar holography. Approximation of variationsin the function of the effective refractive index to the form of atwo-level binary function simplifies production and makes it possible topresent the elements of the holographic pattern in the form ofrectangular elements or dashes that can be easily produced by methods ofmicrolithographic technique. The holographic patterns obtained by themethod have an arrangement different from traditional holographicpatterns and look like a set of the elements randomly distributed overthe plane. However, positions of these elements are most optimal foraccomplishing a given task.

Although the invention has been shown and described with reference tospecific embodiments, it is understood that these embodiments should notbe construed as limiting the areas of application of the invention andthat any changes and modifications are possible, provided that thesechanges and modifications do not depart from the scope of the attachedpatent claims. For example, the choice of the planar optical elements isnot limited by planar laser diodes, planar semiconductor amplifiers, andplanar semiconductor receivers, and may include other elements such asplanar optical modulators, absorbers, or the like. The interconnectingpattern elements of the holographic pattern may have circular,elliptical, or other forms. The substrate can be made from asemiconductor material other than InPGaAs.

1. A method of digitally processing light waves passing through a planarstructure having given functions f_(in)(x, y, ω) and f_(out)(x, y, ω)and consisting of a light-propagating and distributing layer, aplurality of interconnecting pattern elements of a holographic patternin said of light-propagating and distributing layer, and a plurality ofplanar optical elements arranged in a predetermined pattern on theaforementioned light-propagating and distributing layer, the methodcomprising the steps of: calculating positions and shapes of theplurality of interconnecting pattern elements of a holographic patternbased on the aforementioned given functions f_(in)(x, y, ω) andf_(out)(x, y, ω) by a method of solving an inverse problem, saidinterconnecting pattern elements having refractive indices differentfrom the refractive indices of the light-propagating and distributinglayer, said method comprising the steps of: manufacturing theinterconnecting pattern elements of the holographic pattern based on theresults of the calculations; digitizing the aforementioned continuousfunctions${f_{in}( {x,y,\omega} )} \cong {\sum\limits_{n,u}{C_{n\; u}{\exp ( {{ik}_{n}r_{u}} )}{f(\omega)}}}$and${f_{out}( {x,y,\omega} )} \cong {\sum\limits_{m,v}{C_{m\; v}{\exp ( {{- {ik}_{m}}r_{v}} )}{f(\omega)}}}$by providing finite numbers (“n” , “m”, “u”, “v”) of values as a resultof decomposition into the Fourier series; where k_(n), is the wavevector of an incoming wave, and r_(u) is the distance from the incomingport number u to a current point; and _(k) _(m), is the wave vector ofan outgoing wave, and r_(v), is the distance from the outgoing portnumber v to a current point; and using the obtained digitized planarholographic pattern for converting the function f_(in)(x, y, ω) into thefunction f_(out)(x, y, ω).
 2. method of claim 1, wherein manufacturingis carried out by a method selected from microlithography andnanoprinting.
 3. The method of claim 1, wherein the step of calculatingcomprises varying the effective refraction index of Δn(x, y) of theplanar structure for using the effective refraction index of theinterconnecting pattern elements of the holographic pattern differentfrom the effective refraction index of the light-propagating anddistributing layer in order to control directions and properties of thelight beams that propagate through the aforementioned planar structurein accordance with the aforementioned holographic pattern.
 4. The methodof claim 3, wherein the variation of the effective refractive indexΔn(x, y) of the planar structure is made in accordance with formulaΔn(x, y)=∫f _(in)(x, y, ω) f _(out)(x, y, ω) dω. where f_(in)(x, y, ω)and f_(out)(x, y, ω) are the same as defined above.
 5. The method ofclaim 4, wherein variation of the effective refractive index Δn(x, y) isapproximated by a two-level binary function to simplify production. 6.The method of claim 5, wherein the aforementioned interconnectingpattern elements of the holographic pattern are made in the form ofrectangular dashes.
 7. The method of claim 5, wherein the planar opticalelements are selected from planar laser diodes, planar semiconductoramplifiers, and planar semiconductor receivers.